Question

if the perimeter of a circular sector is fixed at 100 ft, what values of r and s give the sector the greatest area?

Answer 1

PLEASE HELP! WE HAVE A QUIZ TMMR AND THIS WILL DECIDE OUR GRADE

Answer 2

write an equation for the area of the sector in terms of r and S, then maximise. bewm.

Answer 3

how do you write the area of a sector?

Answer 4

\[S= {\theta \over360°}\cdot2\pi r\]
area of sector:\[A={\theta \over 360°} \pi r^2\]

Answer 5

how do we find theta?

Answer 6

\[A={S \cdot r \over2}\]

Answer 7

S+r+r=100

Answer 8

so S= 100-2r
so, \[A= {(100-2r)r \over 2}=50r-r^2\]

Answer 9

find the maximum of that.

Answer 10

dude you are a pro! thanks so much!!

Answer 11

you didn't have to find theta, as you can combine the original formulae of arc-S and area-A

You should get r = 25, S=50

Answer 12

yeah thanks! we figured it out :)